Dynamics of a delayed stage-structured fishery management model with impulsive nonlinear harvesting and impulsive birth

Shirui Zhang; Jianjun Jiao; Guiyu Wu; Bingying Gao; Shirui Zhang; Jianjun Jiao; Guiyu Wu; Bingying Gao

doi:10.3934/math.2026650

AIMS Mathematics

2026, Volume 11, Issue 6: 15797-15816. doi: 10.3934/math.2026650

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Dynamics of a delayed stage-structured fishery management model with impulsive nonlinear harvesting and impulsive birth

1.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
2.
School of Big Data Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

Received: 21 March 2026 Revised: 29 April 2026 Accepted: 21 May 2026 Published: 04 June 2026
MSC : 34D23, 37M05, 92D25

Irrational fishing strategies have endangered numerous fish species. The density-dependent harvesting strategy has emerged as one of the potent approaches to address this issue. In this paper, we formulate a fishery management model incorporating the Beddington-DeAngelis functional response and delayed stage structure. The prey population is seasonal birth and impulsive nonlinear harvesting at distinct times. Initially, we show the positivity and the uniform boundedness of solutions in the system. By the comparison theorem of impulsive differential equations, we obtain the global attractivity conditions for the predator-extinction periodic solution. Sufficient conditions for the persistence of the system are derived via constructing the Lyapunov functions and applying other analytical methods. The numerical simulations demonstrate our findings and indicate that impulsive effects, impulsive period and maturation delay have significant influences on the dynamical behaviors of the system. These results provide certain theoretical guidance for sustainable fisheries.
- fishery management,
- impulsive nonlinear harvesting,
- delayed stage-structure,
- Beddington-DeAngelis functional response,
- impulsive birth
Citation: Shirui Zhang, Jianjun Jiao, Guiyu Wu, Bingying Gao. Dynamics of a delayed stage-structured fishery management model with impulsive nonlinear harvesting and impulsive birth[J]. AIMS Mathematics, 2026, 11(6): 15797-15816. doi: 10.3934/math.2026650

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Abstract

Irrational fishing strategies have endangered numerous fish species. The density-dependent harvesting strategy has emerged as one of the potent approaches to address this issue. In this paper, we formulate a fishery management model incorporating the Beddington-DeAngelis functional response and delayed stage structure. The prey population is seasonal birth and impulsive nonlinear harvesting at distinct times. Initially, we show the positivity and the uniform boundedness of solutions in the system. By the comparison theorem of impulsive differential equations, we obtain the global attractivity conditions for the predator-extinction periodic solution. Sufficient conditions for the persistence of the system are derived via constructing the Lyapunov functions and applying other analytical methods. The numerical simulations demonstrate our findings and indicate that impulsive effects, impulsive period and maturation delay have significant influences on the dynamical behaviors of the system. These results provide certain theoretical guidance for sustainable fisheries.

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